The union representing Britain's striking postal workers increased the pressure on Royal Mail management yesterday when it warned there would be a backlog of at least 150m letters and packets if this week's three-day strike went ahead.

The huge volume – up to five times the estimated backlog so far – could take weeks to clear and place acute pressure on the postal system before Christmas. The claim came as both sides agreed to hold talks tomorrow at the TUC following an invitation from its general secretary, Brendan Barber, who helped resolve the last national strike in 2007.

"I have had a number of conversations with Brendan Barber and I'm very pleased we seem to have found a sensible and positive way forward," said the Royal Mail chief executive, Adam Crozier.

The Communication Workers Union (CWU) said 65m letters and packets had to be cleared after last week's two-day strike. The Royal Mail put the figure at around 30m. Mark Higson, Royal Mail's managing director, said workers would start clearing the backlog this week. It has hired 30,000 temporary staff to cope with the demand over the festive period, which has led to claims the recruits will be used as strike breakers.

Yesterday, Royal Mail reiterated its concerns about the impact of the strike. There are fears a number of major customers are switching to alternative carriers. "We are obviously upset at losing any business and will be doing our level best to win it back," Higson said.

But in a move that will dismay the government – which has appealed for both sides to back down – the union warned of weeks of national strikes unless there was progress. Kevin Slocombe, its head of communications, drew comparisons with the strikes of 2007, that were staggered over two months and saw 200m letters delayed. The pile-up, he said, took almost eight weeks to clear.

"We are now entering the Christmas period, when the system comes under intense pressure," he said. "At the end of three days of industrial action we would expect to see 150m letters and packets piling up. It's inevitable that if there is no progress there will be further strikes."

He dismissed claims that the 30,000 temporary workers – double the number usually taken on – could handle the backlog. "They're not trained to deliver so it will really only have a limited effect."

There are fears that Britain is entering months of industrial unrest, as bus drivers, binmen and firefighters follow the postal workers' lead and protest at changes to their pay, shift patterns and working conditions. British Airways and London Underground staff are also considering strike action over pay disputes.

The Unite union representing BA's 14,000 cabin crew could ballot members this week over a Christmas strike. BA announced plans this month to cut 1,700 jobs, enforce a two-year pay freeze and reduce the cabin crew on its 57 Boeing 747s from 15 to 14. Willie Walsh, the chief executive of BA, is refusing to back down.

The RMT rail union is also balloting 10,000 London Underground workers for Christmas strike action after being offered a 1.5% pay rise from April next year, with an additional rise linked to the retail prices index. RMT leader Bob Crow said: "The offer is unacceptable."

Several thousand drivers with FirstGroup, the bus and rail company, will strike tomorrow against a pay freeze. The action will threaten services on routes in Essex, Yorkshire, Wigan, Bolton and Bury.

In Leeds, 600 binmen are starting their eighth week of industrial action. The city council has had to bring in private contractors to shift the waste, at a cost of almost £500,000 so far.

Unrest may spread as other councils introduce employment changes, required by extensions to the Equal Pay Act. Nearly 80% of the 325 councils in England and Wales have reached agreements, but delays at the others hold out the prospect of further strike action.

On Friday, Fire Brigades Union members in South Yorkshire voted in favour of five eight-hour strikes to be held this week over potential job losses. Firefighters on Merseyside have also voted for local strikes, while those in Essex are taking action below strike level.

Crews in Warwickshire, Essex, Hertfordshire, Derbyshire, Cornwall, Lancashire, Leicestershire and Surrey are balloting members over industrial action in response to proposed "efficiency savings" pushed by the Audit Commission and the government. A battle is shaping up in London, where the union is opposing changes to shift patterns. The industrial unrest is the worst in the fire service since the national strike of 2002. "There is a real possibility that these issues could result in national action being taken," said Matt Wrack, general secretary of the FBU.

Hopes that this week's postal strike will be abandoned now hinge on talks at either the TUC or at the conciliation service, Acas. Royal Mail has said it will attend Acas only if the union drops this week's strikes. It accused the union of reneging on a deal last week.

"We felt we had reached an agreement with the CWU on Tuesday," Higson said. "We are calling on them to say they will come in and sign that agreement. We are asking the CWU to live up to the obligations they made."

But the union said it refused to sign after receiving a letter from management which it said undermined the deal.

At the heart of the dispute is a new contract between postal workers and Royal Mail management, signed two years ago, which brought in sweeping changes to pay and working conditions. "Since 2007 we've been attempting to implement the agreement and they've been trying to frustrate it," Higson said.

The union denied this and said it did not want to take further strike action.